Problem: The following line passes through point $(-3, -2)$ : $y = -\dfrac{8}{5} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(-3, -2)$ into the equation gives: $-2 = -\dfrac{8}{5} \cdot -3 + b$ $-2 = \dfrac{24}{5} + b$ $b = -2 - \dfrac{24}{5}$ $b = -\dfrac{34}{5}$ Plugging in $-\dfrac{34}{5}$ for $b$, we get $y = -\dfrac{8}{5} x - \dfrac{34}{5}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-3, -2)$